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Simplifying (x + 3)(x + -7) + -1(x + 5) = 0 Reorder the terms: (3 + x)(x + -7) + -1(x + 5) = 0 Reorder the terms: (3 + x)(-7 + x) + -1(x + 5) = 0 Multiply (3 + x) * (-7 + x) (3(-7 + x) + x(-7 + x)) + -1(x + 5) = 0 ((-7 * 3 + x * 3) + x(-7 + x)) + -1(x + 5) = 0 ((-21 + 3x) + x(-7 + x)) + -1(x + 5) = 0 (-21 + 3x + (-7 * x + x * x)) + -1(x + 5) = 0 (-21 + 3x + (-7x + x2)) + -1(x + 5) = 0 Combine like terms: 3x + -7x = -4x (-21 + -4x + x2) + -1(x + 5) = 0 Reorder the terms: -21 + -4x + x2 + -1(5 + x) = 0 -21 + -4x + x2 + (5 * -1 + x * -1) = 0 -21 + -4x + x2 + (-5 + -1x) = 0 Reorder the terms: -21 + -5 + -4x + -1x + x2 = 0 Combine like terms: -21 + -5 = -26 -26 + -4x + -1x + x2 = 0 Combine like terms: -4x + -1x = -5x -26 + -5x + x2 = 0 Solving -26 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -5x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -5x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -5x + x2 = 0 + 26 -5x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -5x + x2 = 26 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 26 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 26 + 6.25 Combine like terms: 26 + 6.25 = 32.25 6.25 + -5x + x2 = 32.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -2.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -2.5 = 5.678908346 Simplifying x + -2.5 = 5.678908346 Reorder the terms: -2.5 + x = 5.678908346 Solving -2.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.678908346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.678908346 + 2.5 x = 5.678908346 + 2.5 Combine like terms: 5.678908346 + 2.5 = 8.178908346 x = 8.178908346 Simplifying x = 8.178908346Subproblem 2
x + -2.5 = -5.678908346 Simplifying x + -2.5 = -5.678908346 Reorder the terms: -2.5 + x = -5.678908346 Solving -2.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.678908346 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.678908346 + 2.5 x = -5.678908346 + 2.5 Combine like terms: -5.678908346 + 2.5 = -3.178908346 x = -3.178908346 Simplifying x = -3.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.178908346, -3.178908346}
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